Question

$\huge \bf Question$

✯ A ball is thrown vertically upwards with a velocity of 49m/s. Calculate,

➷ the maximum height to which it rises.

➷ the total time it takes to return to the surface of the earth.​

Answer 1

QUESTION

A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate (1) The maximum height to which it rises. (2) The total time it takes to return to the surface of the earth.

ANSWER

Given parameters

Initial velocity of the ball (u) = 49m/s.

The velocity of the ball at maximum height (v) = 0.

g = 9.8m/s2

Let us considered the time taken is t to reach the maximum height H.

Consider a formula,

2gH = v2 – u2

2 × (- 9.8) × H = 0 – (49)2

– 19.6 H = – 2401

H = 122.5 m

Now consider a formula,

v = u + g × t

0 = 49 + (- 9.8) × t

– 49 = – 9.8t

t = 5 sec

(1) The maximum height to ball rises = 122.5 m

(2) The total time ball takes to return to the surface of the earth = 5 + 5 = 10 sec.

Explanation:

I hope it helps ✌✌

Answer 2

⇒ Given:

A ball is thrown vertically upwards with a velocity of 49 m/s.

⇒ To Find:

The maximum height to which it rises.

The total time it takes to return to the surface of the earth.

⇒ Formulae to be used:

→ 2gh = v² - u² [Taken from v² - u² = 2as]

→ v = u + gt [Taken from v = u + at]

⇒ Solution:

Let the initial velocity, u = 49 m/s

Final velocity, v = 0

g = 9.8 m/s

h = to be found

t = to be found

✳ To find the maximum height to which it rises.

Here, we can use the formula v² - u² = 2gh

0² - 49² = 2 x -9.8 x h

-2401 = -19.6h

$\sf{\dfrac{-2401}{-19.6}=h}$

h = 122.5 m

✳ To find the total time it takes to return to the surface of the earth.

Here, we can use the formula v = u + gt

0 = 49 + -9.8t

-49 = -9.8t

$\sf{\dfrac{-49}{-9.8}=t}$

t = 5 seconds

The given time refers to the time covered by the ball in one direction. The total distance covered by the ball is

5 + 5 = 10 seconds

⇒ Final answers:

The maximum height to which the ball travels = 122.5 m

The total time taken by the ball = 10 seconds

Note:

We have taken g as -9.8 m/s as we had to find the values when the ball was thrown upwards. Gravity always act in the downward direction and while solving numerals where we have to find values when thrown upwards, we need to take the negative.